Numerical study by a controllability method for the calculation of the time-periodic solutions of the Maxwell and Vlasov-Maxwell systems

 Access to full text

 Full (PDF)

1. [1] A. Arsenev, Global existence of a weak solution of Vlasov’s system of equations. USSR Comp. Math. Math. Phys. 15 (1975) 131–143. 
2. [2] K. Asano and S. Ukai, On the Vlasov-Poisson limit of the Vlasov-Maxwell equation. Pattern and waves. Qualitative analysis of nonlinear differential equations. Stud. Math. Appl. 18 (1986) 369–383. Zbl0623.35059
3. [3] N. Ben.Abdallah, Weak solutions of the initial-boundary value problem for the Vlasov-Poisson system,. Math. Meth. Appl. Sci. 17 (1994) 451–476. Zbl0806.35172
4. [4] M. Bezard, Boundary value problems for the Vlasov-Maxwell system, in Semin. Équ. Deriv. Partielles, Ec. Polytech., Cent. Math., Palaiseau Semi 1992–1993, Exp. No. 4 (1993) 17. Zbl0878.35107
5. [5] B. Bodin, Modélisation et simulation numérique du régime de Child-Langmuir. Thèse de l’École Polytechnique, Palaiseau (1995). 
6. [6] M. Bostan and F. Poupaud, Periodic solutions of the Vlasov-Poisson system with boundary conditions. C. R. Acad. Sci. Paris, Sér. I 325 (1997) 1333–1336. Zbl0895.35079
7. [7] M. Bostan and F. Poupaud, Periodic solutions of the Vlasov-Poisson system with boundary conditions. Math. Mod. Meth. Appl. Sci. 10 (1998) 651–672. Zbl1019.76047
8. [8] M. Bostan and F. Poupaud, Periodic solutions of the 1D Vlasov-Maxwell system with boundary conditions. Math. Meth. Appl. Sci. 23 (2000) 1195–1221. Zbl0965.35010
9. [9] M.O. Bristeau, R. Glowinski and J. Périaux, Controllability methods for the computation of time periodic solutions; application to scattering. J. Comp. Phys. 147 (1998) 265–292. Zbl0926.65054
10. [10] J.P. Cioni, Résolution numérique des équations de Maxwell instationnaires par une méthode de volumes finis. Ph.D., Université de Nice Sophia-Antipolis (1995). 
11. [11] J.P. Cioni, L. Fezoui and D. Issautier, High-order upwind schemes for solving time-domain Maxwell equation. La Recherche Aérospatiale No. 5 (1994) 319–328. 
12. [12] P. Degond, Regularité de la solution des équations cinétiques en physiques de plasmas, in Semin. Équ. Dériv. Partielles 1985–1986, Exp. No. 18 (1986) 11. Zbl0613.35070
13. [13] P. Degond, Local existence of solutions of the Vlasov-Maxwell equations and convergence to the Vlasov-Poisson equations for infinite light velocity. Math. Methods Appl. Sci. 8 (1986) 533–558. Zbl0619.35088
14. [14] P. Degond, Global existence of smooth solutions for the Vlasov-Fokker-Planck equation in 1 and 2 space dimensions. Ann. Sci. Ec. Norm. Super. IV. Ser. 19 (1986) 519–542. Zbl0619.35087
15. [15] R.J. Diperna and P.L. Lions, Global weak solutions of Vlasov-Maxwell system. Comm. Pure Appl. Math. XVII (1989) 729–757. Zbl0698.35128
16. [16] C. Greengard and P.A. Raviart, A boundary value problem for the stationary Vlasov-Poisson system. Comm. Pure Appl. Math. XLIII (1990) 473–507. Zbl0721.35084
17. [17] Y. Guo, Global weak solutions of the Vlasov-Maxwell system with boundary conditions. Comm. Math. Phys. 154 (1993) 245–263. Zbl0787.35072
18. [18] Y. Guo, Regularity for the Vlasov equation in a half space. Indiana Univ. Math. J. 43 (1994) 255–320. Zbl0799.35031
19. [19] P.L. Lions and B. Perthame, Propagation of moments and regularity for the 3-dimensional Vlasov-Poisson system. Invent. Math. 105 (1991) 415–430. Zbl0741.35061
20. [20] R. Löhner and J. Ambrosiano, A finite element solver for the Maxwell equations, in GAMNI-SMAI conference on numerical methods for the solution of Maxwell equations, Paris (1989). 
21. [21] K. Pfaffelmoser, Global classical solutions of the Vlasov-Poisson system in 3 dimensions for general initial data. J. Diff. Eq. 95 (1992) 281–303. Zbl0810.35089
22. [22] F. Poupaud, Boundary value problems for the stationary Vlasov-Maxwell system. Forum Math. 4 (1992) 499–527. Zbl0785.35020